Rots and Refs

Follow hints using a little coordinate geometry, plane geometry and trig to see how matrices are used to work on transformations of the plane.

Reflect Again

Follow hints to investigate the matrix which gives a reflection of the plane in the line y=tanx. Show that the combination of two reflections in intersecting lines is a rotation.

Transformations for 10

Explore the properties of matrix transformations with these 10 stimulating questions.

The Matrix

Stage: 5 Challenge Level:
The point $P=(x,y)$ has image $P'=(ax+by, cx+dy)$. Draw diagrams and consider the effect of the transformation on the line $OP$ joining $P$ to the origin.